Zorn’s lemma

Note that the empty chain in X has an upper bound in X
if and only if X is non-empty.
Because this case is rather different from the case of non-empty chains,
Zorn’s Lemma is often stated in the following form:
If X is a non-empty partially ordered set
such that every non-empty chain in X has an upper bound,
then X has a maximal element.
(In other words: Any non-empty inductively ordered set has a maximal element.)